Minicourse on minimal surfaces in hyperbolic manifolds: CMC hypersurfaces of finite index and Do Carmo’s question in $\mathbb{R}^6$

Speaker:Han Hong (Beijing Jiaotong University)

Time: 2025-06-26 14:00
Location: R1010, SIMIS

Abstract:
In this talk, we will show that complete noncompact constant mean curvature hypersurfaces in $\mathbb{R}^6$ with finite index must be minimal. This result provides a positive answer to do Carmo’s question in dimension $6$. The proof is also applicable to $\mathbb{R}^4$ and $\mathbb{R}^5$, thereby providing alternative proofs for those previously resolved cases. This is a joint work with Jingche chen and Haizhong Li.